Question 865830
This is a uniform rates of work problem.


The job is, "reply to a days worth of customer emails".  That is 1 job.  Create expressions or numbers for each worker's work rate as jobs per time.   You need to translate from the description into number expressions.


Let x = time in hours for Cheri to do 1 job herself, alone.
Dani, {{{1/(x+6)}}}
Cheri, {{{1/x}}}
Dani And Cheri Together, {{{1/4}}}


The rate for both workers "together" is the sum of their individual rates.
{{{highlight_green(1/x+1/(x+6)=1/4)}}}.
Solve this equation for x.  You WILL obtain a quadratic equation in the solving process. Begin by multiplying the left side and right side by {{{4x(x+6)}}}, which is the simplest common denominator; and this will clear the denominators.